Dans cet article, nous prouvons l’existence d’une solution pour le problème de Stokes compressible stationnaire en tenant compte, en particulier, des effets gravitaires. L’équation d’état donne la pression comme une fonction strictement croissante superlinéaire de la densité. L’existence de solution est obtenue en passant à la limite sur une approximation visqueuse de l’équation de continuité.
In this paper, we prove the existence of a solution for a quite general stationary compressible Stokes problem including, in particular, gravity effects. The Equation Of State gives the pressure as an increasing superlinear function of the density. This existence result is obtained by passing to the limit on the solution of a viscous approximation of the continuity equation.
@article{AFST_2014_6_23_4_847_0,
author = {Fettah, A. and Gallou\"et, T. and Lakehal, H.},
title = {An existence proof for the stationary compressible {Stokes} problem},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {847--875},
publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 23},
number = {4},
year = {2014},
doi = {10.5802/afst.1427},
zbl = {06374891},
mrnumber = {3270426},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/afst.1427/}
}
TY - JOUR AU - Fettah, A. AU - Gallouët, T. AU - Lakehal, H. TI - An existence proof for the stationary compressible Stokes problem JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2014 SP - 847 EP - 875 VL - 23 IS - 4 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://archive.numdam.org/articles/10.5802/afst.1427/ DO - 10.5802/afst.1427 LA - en ID - AFST_2014_6_23_4_847_0 ER -
%0 Journal Article %A Fettah, A. %A Gallouët, T. %A Lakehal, H. %T An existence proof for the stationary compressible Stokes problem %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2014 %P 847-875 %V 23 %N 4 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://archive.numdam.org/articles/10.5802/afst.1427/ %R 10.5802/afst.1427 %G en %F AFST_2014_6_23_4_847_0
Fettah, A.; Gallouët, T.; Lakehal, H. An existence proof for the stationary compressible Stokes problem. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 23 (2014) no. 4, pp. 847-875. doi : 10.5802/afst.1427. http://archive.numdam.org/articles/10.5802/afst.1427/
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